build tree using traversals

Author: Sai-Adithya-M

data_structures/binary_tree/build_tree_from_traversal.py

@@ -0,0 +1,105 @@
+# Binary Tree Node class
+class Node:
+    def __init__(self, data):
+        self.data = data
+        self.left = None
+        self.right = None
+
+
+# Normal inorder traversal
+def inorder(root, out):
+    """Perform inorder traversal and append values to 'out' list."""
+    if root is None:
+        return
+    inorder(root.left, out)
+    out.append(root.data)
+    inorder(root.right, out)
+
+
+# === Build tree using PREORDER + INORDER ===
+def build_tree_from_pre(preorder, pre_start, pre_end,
+                        inorder_seq, in_start, in_end, in_map):
+    """Recursive helper to build tree from preorder and inorder traversal."""
+    if pre_start > pre_end or in_start > in_end:
+        return None
+
+    # Root is the first element in current preorder segment
+    root_val = preorder[pre_start]
+    root = Node(root_val)
+
+    # Find the root index in inorder traversal
+    in_root_index = in_map[root_val]
+    nums_left = in_root_index - in_start
+
+    # Recursively build left and right subtrees
+    root.left = build_tree_from_pre(
+        preorder, pre_start + 1, pre_start + nums_left,
+        inorder_seq, in_start, in_root_index - 1, in_map)
+
+    root.right = build_tree_from_pre(
+        preorder, pre_start + nums_left + 1, pre_end,
+        inorder_seq, in_root_index + 1, in_end, in_map)
+
+    return root
+
+
+def build_tree_pre(inorder_seq, preorder_seq):
+    """Wrapper function for building tree from preorder + inorder."""
+    in_map = {val: i for i, val in enumerate(inorder_seq)}
+    return build_tree_from_pre(
+        preorder_seq, 0, len(preorder_seq) - 1,
+        inorder_seq, 0, len(inorder_seq) - 1, in_map)
+
+
+# === Build tree using POSTORDER + INORDER ===
+def build_tree_from_post(postorder, post_start, post_end,
+                         inorder_seq, in_start, in_end, in_map):
+    """Recursive helper to build tree from postorder and inorder traversal."""
+    if post_start > post_end or in_start > in_end:
+        return None
+
+    # Root is the last element in current postorder segment
+    root_val = postorder[post_end]
+    root = Node(root_val)
+
+    # Find the root index in inorder traversal
+    in_root_index = in_map[root_val]
+    nums_left = in_root_index - in_start
+
+    # Recursively build left and right subtrees
+    root.left = build_tree_from_post(
+        postorder, post_start, post_start + nums_left - 1,
+        inorder_seq, in_start, in_root_index - 1, in_map)
+
+    root.right = build_tree_from_post(
+        postorder, post_start + nums_left, post_end - 1,
+        inorder_seq, in_root_index + 1, in_end, in_map)
+
+    return root
+
+
+def build_tree_post(inorder_seq, postorder_seq):
+    """Wrapper function for building tree from postorder + inorder."""
+    in_map = {val: i for i, val in enumerate(inorder_seq)}
+    return build_tree_from_post(
+        postorder_seq, 0, len(postorder_seq) - 1,
+        inorder_seq, 0, len(inorder_seq) - 1, in_map)
+
+
+# === Example ===
+if __name__ == "__main__":
+    inorder_seq = [1, 2, 3, 4, 5]
+    preorder_seq = [3, 2, 1, 4, 5]
+    postorder_seq = [1, 2, 5, 4, 3]
+
+    print("=== Build BST from Preorder & Inorder ===")
+    tree_pre = build_tree_pre(inorder_seq, preorder_seq)
+    out = []
+    inorder(tree_pre, out)
+    print("Inorder:", *out)
+
+    print("=== Build BST from Postorder & Inorder ===")
+    tree_post = build_tree_post(inorder_seq, postorder_seq)
+    out = []
+    inorder(tree_post, out)
+    print("Inorder:", *out)